Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 15 - Multiple Integrals - 15.6 Triple Integrals - 15.6 Exercises - Page 1077: 13



Work Step by Step

Let us consider that $I=\iiint_E 6xy dV$ Thus, $I= \int_{0}^1 \int_{0}^{\sqrt x} \int_{0}^{1+x+y} (6xy) dz dy dx$ Further, we have $\int_{0}^1\int_{0}^{\sqrt x} |6xyz|_{0}^{1+x+y} dy dx=\int_{0}^1\int_{0}^{\sqrt x} (6xy+6x^2y+6xy^2) dy dx$ or, $=\int_0^1 [3xy^2+3x^2y^2+2xy^3]_{0}^{\sqrt x}dx$ or, $ \int^{0}_{1} 3x^2+3x^3+2x^{5/2} dx= [\dfrac{3x^3}{3}+\dfrac{3x^4}{4}+(2)(2/7)x^{7/2}]^{0}_{1}$ or, $=\dfrac{65}{28}$
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